AIEEE 2006 Mock Test

The set of points where $f(x)=\frac{x}{1+|x|}$ is differentiable is:

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $x$. The maximum area enclosed by the park is:

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are $10$ candidates and $4$ are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is:

If the expansion in powers of $x$ of the function $\frac{1}{(1-ax)(1-bx)}$ is $a_0+a_{1}x+a_2{x}^2+a_3{x}^3+\dots$, then $a_n$ is:

For natural numbers $m,n$, if $(1-y{)}^m(1+y{)}^n=1+a_{1}y+a_2{y}^2+\dots$, and $a_1=a_2=10$, then $(m,n)$ is: